Find and classify all critical points of the function 5 f (x, y, z, w) = x² + y? + 3z2 + w² + 3xy+ 6xz + 5xw + 4yz + 2yw + 5x – 3y + 6w. 2 Note that your solutions might not be integers.

Q: o pass the course, a student must achieve at least a general average of 75 points in 3 major exams.…

A: Given: Required general average score in 3 major is 75 points. Score in two of the subjects is 70…

Q: A group of students were asked whether they like Mathematics, Physics, or both. If 456 like…

A: We want to find total number of students.

Q: (b) x" – 2x' + x = 4e'.

A:

Q: Q.3- Prove that: 2n 1 (cos =0 +i sin €) + 10 2cosne eine

A:

Q: Jse the Limit Comparison Test to determine the convergence or divergence of the series. 1 8) n/n +1

A:

Q: 10. A game of chance involves a spinner marked with mimbers from 1-30. The game costs $10 to play.…

A:

Q: 10+ j5+3Z40° +10Z30° - 3+ j4

A:

Q: What value of t ensures the following system of equations has no solution? Зи + (? — 4)у = 1 ty = 2…

A: We want to find value of t for which system has no solution.

Q: Find the area of the shaded region. Vcos 20 r = 2 cos 0 NOTE: Enter the exact answer. A ||

A:

Q: 6. Let a > 0 and let R be the region under the graph of f(x) 9- ax and in the first quadrant. Find a…

A: We will find intersecting point and then draw region bounded by graphs . Then by integration find…

Q: Which of the following matrices is not in reduced row-echelon form ? 10 0 4-) 0 0 1 5 0 0 0 0 1 1 0…

A: We want to find the matrix which is not in reduced row-echelon form

Q: Find the draganalictle rohx A that ene eegmpars.

A: Given λ1 = 2,  v1 = 11λ2 = 3,  v2 = 21

Q: Exercise 14.6.10. Prove that it is impossible to write the identity permu- tation as the product of…

A: We have to show it is impossible to write the identity permutation as the product of an odd number…

Q: Consider the ordered bases B = ((-1,7), (1, –8)) and C = ((0, –2), (4, –3)) for the vector space R².…

A:

Q: What value of t ensures the following system of equations has infinitely many solutions? ... 3r + (*…

A: Given system of equation is 3x + (t2 - 4)y = 1ty = 2

Q: Consider the following function 5z2 – 4z +3 f (2) = (z + 1) (z + 2) (z +3) Find the residue at each…

A:

Q: What is the result of applying the row operations –3R1 + R2 → R2 and -R1 + R3 → R3 to the matrix 2…

A: Row operations are calculations we can do using the rows of a matrix in order to solve a system of…

Q: Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in the…

A: (a) {x2 : x ∈ S3}    = { e2, (1 2)2, (1 3)2, (2 3)2, (1 2 3)2, (1 3 2)2}    = {e, e, e, e, (1 3 2),…

Q: Two gallons of mango juice fills up 15 glasses . How many millimeter of juice are needed to fill up…

A: 2 gallons of mango juice fills up 15 glasses.

Q: As shown the figure, solve for the area of the region R enclosed by the graphs of f and g with the…

A: Area bounded by the curves, using integrals

Q: Collect like terms and write in descending order 5x4 + 4x2 - 3x4 1. 6x10 2. 6x2 3. Can't be…

A: Given expression: 5x4+4x2-3x4 To determine: Simplify the expression and write like terms in…

Q: Question 2. Approximate the roots of the polynomial f(x) = X° - 7X + 6 using False-position method.

A: To approximate the root of the equation using false position method .

Q: The figure below is dilated with the center of dilation at the orgin and a scale factor of 1/2. What…

A: By graph we can see that  B = (2, - 4) Scale Factor  = 1/2 = 0.5

Q: 4. In each part below, give an example of a function which satisfies the given criteria. Justify…

A: (i) Find an example for a function f whose domain is -1, 1 such that limx→0+fx=3 and limx→0-fx=-2.…

Q: find the general Solutin xCE\ OP the syctem -47 /4 2. G ļ Cz are anbytory con <ləts,

A:

Q: The following data is given: 1 3 4 9. 12 14 y 2 4 5 7 9 11 Use linear least-squares regression to…

A:

Q: For skew anti-symmetric matrix, the sum of its entries is (A 1 В -5 10 E -1

A: We want to find sum of entries of skew anti-symmetric matrix.

Q: Determime the type of crtiek |(x. iXz) =(½,) of the System. v'efx, where x=[ point non inesr %3D…

A:

Q: Use the shell method to set up and evaluate an integral that gives the volume of the solid generated…

A:

Q: Which of the following is longer than 600 meters? * 60 dekameters 23,000 inches 2,000 feet 600 yards

A: Solution

Q: Find the Inverse of the following matrix: 1 07 A = -1 2 -2 A-1 = NOTE: the entries in the inverse…

A:

Q: Given T-1 = (2 + y)i + (x – 3y)j what is the value of det T|? 07 O-7 O 17 O -1/7

A:

Q: 4. Show the vector field Vu x Vv, where u and v are scalar fields, is solenoidal.

A:

Q: Use the method of undetermined coefficients to solve the differential equations

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: rea of the closed region det

A: Given, the equation of the circle is                                        (x+2)2+(y-3)2=4

Q: You want to buy a $136,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan…

A: a) Given that, the down payment is 20% of $136,000. That is,DP=$136,000×20100.…

Q: Write the equation of a sine or cosine function to describe the graph. y = || -1+ -2- 3- -4+

A: Consider the graph of y=sin x and y=cos x. The given graph resembles the graph of y=sin x. So, let…

Q: If A and B be 2 x 2 matrices, then (A +B)(A – B) = A² – B². A True B False

A:

Q: Use Laplace transforms to solve the initial value problems: (a) x" + 9x = 0; x(0) = 3, x'(0) = 4

A:

Q: 4. In each part below, give an example of a function which satisfies the given criteria. Justify…

A: (i) Here we have to find a function whose domain is -1, 1 such that limx→0+fx=3, limx→0-fx=-2

Q: и Write the vector shown below as a combination of vectors ū and v shown above

A: Solution

Q: Which of the following matrices is not in row-echelon form? (:) 10 2 4Y 0 0 1 5 0 0 10 W1 0 2 4 B)…

A:

Q: 7. Find the remainder when 4197 is divided by 13.

A:

Q: Let A = and U = Then A2017U is equal to ... B

A:

Q: Question 16 Let A = - The eigenvalues of A (listed in increasing order) are 11 and All answers are…

A:

Q: A survey of 150 people was conducted to determine their favorite sport. 74 people like chess, 94…

A: We want to find number of people that not like any of the three sports.

Q: **Use the following five trigonometric equations to answer questions 2 and 3 below.*** Equation 1:…

A:

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

Q: in all possible values for z.

A:

Q: 1 1 -1 e the Eigen

A: